INCORRECT - see explanation
Note: Arrays.asList() will create a NEW list with the contents of the passed array. The original array will not be modified at all when you use Collections.shuffle().
Explanation
Peter has correctly pointed our that Arrays.asList() does NOT make a copy. The returned list is "write-through" back to the original array. Shuffling the list will shuffle the contents of the original array. Also worth noting that the list is immutable (new elements cannot be added) but typically I find that the use of Arrays.asList() involves immutable lists anyway.
files.get(0); // get the first elements in shuffled list, random
// as greg said
int index = files.indexOf(a[0]); // find out where "image1.txt" is in the list
files.get(index); // get "image1.txt" back from the list